Normal Distribution Calculations Using Technology
All of the calculations that we will do in Math 180A involving the normal distribution can
be done using tables. A normal distribution table will be provided on exams. However, it
is recommended that you also learn how to make these calculations using either a graphing
calculator or Microsoft Excel.
Below are some instructions. On the TI-83, you can follow these instructions as soon as you
turn on your calculator. On the TI-89, you first have to press APPS, then select FlashApps, then
scroll to Stats/List Editor, then press Enter twice. You should then see options ranging from
F1-Tools to F7-Ints, and you are ready to follow the instructions below.
It will often be necessary to calculate probabilities of the form P (Z ≤ z), P (Z ≥ z), or
P (a ≤ Z ≤ b), where Z has a standard normal distribution.
Microsoft Excel: Using Microsoft Excel, you can find probabilities of the form P (Z ≤ z). For
example, to find P (Z ≤ 1.26), type “=normsdist(1.26)” into a cell, and you should get .8962.
To find other probabilities, you can convert them into the form P (Z ≤ z). For example, to find
P (Z ≥ −0.37), observe that this is 1−P (Z ≤ −0.37), so you can type “1 - normsdist(-0.37)” to get
the answer of .6443. To find P (−0.37 ≤ Z ≤ 1.26), you can calculate P (Z ≤ 1.26)−P (Z ≤ −0.37)
by typing “=normsdist(1.26) - normsdist(-0.37)” to get the answer of .5405.
TI-83: Press DISTR (that is, 2nd and VARS), and choose 2:normalcdf. To calculate P (−0.37 ≤
Z ≤ 1.26), type “-0.37, 1.26, 0, 1)” to finish the command, then press ENTER. The numbers 0 and
1 that are entered correspond to the mean and standard deviation of Z respectively. You should
obtain an answer of .5405. The TI-83 only calculates probabilities of the form P (a ≤ Z ≤ b) and
not of the form P (Z ≤ z) or P (Z ≥ z). However, to find P (Z ≤ 1.26), you can type a number
such as −100 for the lower endpoint, so the full command becomes normcdf(-100, 1.26, 0, 1). To
find P (Z ≥ −0.37), use 100 for the upper endpoint.
TI-89: Press F5, then scroll down to 4:normal Cdf. Then input the four numbers requested,
moving from each number to the next one using the down arrow. To find P (−0.37 ≤ Z ≤ 1.26),
enter -0.37 for the Lower Value, 1.26 for the Upper Value, 0 for the mean µ, and 1 for the standard
deviation σ. To find P (Z ≤ 1.26), use a number such as -100 for the Lower Value and 1.26 for
the Upper Value. To find P (Z ≥ −0.37), use -0.37 for the Lower Value and 100 for the Upper
Value.
In some problems, it will be necessary, for a given value y, to find the value of z such that
P (Z ≤ z) = y. These are known as inverse normal calculations and can be carried out using the
instructions below.
Microsoft Excel: To find the value of z such that P (Z ≤ z) = .95, type “=normsinv(.95)” into
a cell to get the answer of 1.645. That is, 95 percent of the area under the normal curve is to the
left of 1.645.
TI-83: Press DISTR (that is, 2nd and VARS), and choose 3:invnorm. The command “invNorm(”
should appear. To finish the command, type “.95, 0, 1)” to get the answer of 1.645. This means
that P (Z ≤ 1.645) ≈ .95.
TI-89: Press F5, then scroll down to 2:Inverse, then select 1:Inverse Normal. Type .95 for Area,
0 for µ, and 1 for σ to get the answer of 1.645. This means that P (Z ≤ 1.645) ≈ .95.